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An '''elementary proof''' or '''elementary technique''' in mathematics is a [[proof]] that uses only [[real numbers]] or [[real analysis]] rather than the use of [[complex analysis]].<ref>http://mathworld.wolfram.com/ElementaryProof.html</ref> Elementary proofs cannot be broken down into smaller proofs of the same proposition.

An '''elementary proof''' or '''elementary technique''' in mathematics is a [[proof]] that uses only [[real numbers]] or [[real analysis]] rather than the use of [[complex analysis]].<ref>http://mathworld.wolfram.com/ElementaryProof.html</ref> Elementary proofs cannot be broken down into smaller proofs of the same proposition.

The [[Prime Number Theorem]] has long been proven using complex analysis ([[Riemann Zeta function]]), but in 1949 and 1950 an elementary proof by [[Paul Erdos]] and [[Atle Selberg]] earned Selberg the highest prize in math, the [[Fields Medal]]. In contrast, [[Andrew Wiles]]' proof of [[Fermat's Last Theorem]] did not use elementary techniques. Wiles did not receive the Fields Medal for his exceptional work because he was 41 years old when he published his proof of Fermat's Last Theorem and was therefore ineligible for the Fields Medal, which is awarded only to mathematicians no older than 40.<ref>http://www.princeton.edu/pr/news/98/q3/0827-wiles.html</ref>)

The [[Prime Number Theorem]] has long been proven using complex analysis ([[Riemann Zeta function]]), but in 1949 and 1950 an elementary proof by [[Paul Erdos]] and [[Atle Selberg]] earned Selberg the highest prize in math, the [[Fields Medal]]. In contrast, [[Andrew Wiles]]' proof of [[Fermat's Last Theorem]] did not use elementary techniques.

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